Details

Time bar (total: 16.8s)

analyze2.2s (12.8%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
1.6%98.3%0.1%8
2.3%97.5%0.1%9
7.4%90.9%1.7%10
9.2%87.4%3.5%11
11.7%83.5%4.8%12
15.2%76%8.8%13
16.4%72%11.6%14
Compiler

Compiled 26 to 22 computations (15.4% saved)

sample123.0ms (0.7%)

Algorithm
1×intervals
Results
63.0ms100×body1024valid
19.0ms108×body128valid
12.0ms29×body512valid
5.0ms19×body256valid
5.0ms41×body128invalid
2.0ms5×body512invalid
2.0ms3×body1024invalid
1.0ms4×body256invalid
Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify228.0ms (1.4%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
0492835
1492835

prune8.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 32.7b

Counts
2 → 1
Compiler

Compiled 94 to 78 computations (17% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.0b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
3.2b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
14.3b
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
17.5b
(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite84.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
108×add-exp-log_binary64_461
58×prod-exp_binary64_472
52×add-cbrt-cube_binary64_459
28×times-frac_binary64_429
26×add-sqr-sqrt_binary64_445 cbrt-unprod_binary64_456
24×div-exp_binary64_474
20×pow1_binary64_484
19×*-un-lft-identity_binary64_423
18×associate-*l*_binary64_364
17×add-cube-cbrt_binary64_458
16×associate-*l/_binary64_366
12×associate-/l*_binary64_368
10×pow-prod-down_binary64_494 frac-times_binary64_433 associate-*r*_binary64_363 cube-prod_binary64_451 unpow-prod-down_binary64_502
8×pow-to-exp_binary64_492 pow-exp_binary64_491 tan-quot_binary64_582 cbrt-undiv_binary64_457
6×associate-*r/_binary64_365
5×unswap-sqr_binary64_391
4×flip-+_binary64_397 flip3-+_binary64_426 add-log-exp_binary64_462 sqr-pow_binary64_395
3×unpow3_binary64_489 *-commutative_binary64_354 cube-mult_binary64_453
2×div-inv_binary64_420
1×distribute-rgt-in_binary64_373 distribute-lft-in_binary64_372 distribute-lft-out_binary64_374 clear-num_binary64_422 frac-2neg_binary64_434 associate-/r*_binary64_367
Counts
4 → 159
Calls

4 calls:

27.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
16.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
14.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
8.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

series1.2s (7.2%)

Counts
4 → 12
Calls

4 calls:

710.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
343.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
115.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
45.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify70.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
055923677

prune728.0ms (4.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1629171
Fresh000
Picked101
Done000
Total1639172

Merged error: 16.3b

Counts
172 → 9
Compiler

Compiled 13298 to 9053 computations (31.9% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.0b
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k))
4.6b
(*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))
9.0b
(/.f64 (*.f64 t t) l)
14.3b
(*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite88.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
113×add-exp-log_binary64_461 add-cbrt-cube_binary64_459
65×prod-exp_binary64_472 cbrt-unprod_binary64_456
44×associate-*l/_binary64_366
34×frac-times_binary64_433
29×pow1_binary64_484
20×cbrt-undiv_binary64_457 div-exp_binary64_474
17×pow-prod-down_binary64_494
16×tan-quot_binary64_582
15×add-sqr-sqrt_binary64_445
14×associate-*r/_binary64_365
13×*-un-lft-identity_binary64_423
11×add-cube-cbrt_binary64_458
10×associate-*r*_binary64_363
9×associate-*l*_binary64_364
8×flip-+_binary64_397 flip3-+_binary64_426
7×times-frac_binary64_429
4×add-log-exp_binary64_462
3×*-commutative_binary64_354 associate-/r*_binary64_367
2×div-inv_binary64_420 unswap-sqr_binary64_391
1×distribute-rgt-in_binary64_373 distribute-lft-in_binary64_372 distribute-lft-out_binary64_374 clear-num_binary64_422 frac-2neg_binary64_434 associate-/l*_binary64_368
Counts
4 → 151
Calls

4 calls:

34.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
16.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k))
9.0ms
(*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))
5.0ms
(/.f64 (*.f64 t t) l)

series1.2s (7.1%)

Counts
4 → 12
Calls

4 calls:

733.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
337.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k))
107.0ms
(*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))
26.0ms
(/.f64 (*.f64 t t) l)

simplify107.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
050134012

prune619.0ms (3.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1558163
Fresh538
Picked101
Done000
Total16111172

Merged error: 10.9b

Counts
172 → 11
Compiler

Compiled 11997 to 7600 computations (36.7% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
3.0b
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
3.3b
(*.f64 (/.f64 t l) (sin.f64 k))
14.3b
(*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite185.0ms (1.1%)

Algorithm
1×rewrite-expression-head
Rules
421×add-exp-log_binary64_461
304×add-cbrt-cube_binary64_459
259×prod-exp_binary64_472
181×cbrt-unprod_binary64_456
179×frac-times_binary64_433
178×associate-*l/_binary64_366
108×div-exp_binary64_474
81×associate-*r/_binary64_365
69×cbrt-undiv_binary64_457
56×tan-quot_binary64_582
47×associate-/r/_binary64_369
40×pow1_binary64_484
32×flip-+_binary64_397 flip3-+_binary64_426
26×pow-prod-down_binary64_494
21×add-sqr-sqrt_binary64_445
18×*-un-lft-identity_binary64_423 1-exp_binary64_467
16×add-cube-cbrt_binary64_458
15×associate-*l*_binary64_364
13×times-frac_binary64_429
10×associate-*r*_binary64_363
4×add-log-exp_binary64_462
3×*-commutative_binary64_354 associate-/l*_binary64_368
2×div-inv_binary64_420 unswap-sqr_binary64_391
1×distribute-rgt-in_binary64_373 distribute-lft-in_binary64_372 distribute-lft-out_binary64_374 clear-num_binary64_422 frac-2neg_binary64_434 associate-/r*_binary64_367
Counts
4 → 308
Calls

4 calls:

42.0ms
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
42.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
22.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
8.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series1.7s (10.2%)

Counts
4 → 12
Calls

4 calls:

731.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
530.0ms
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
346.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
103.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

simplify161.0ms (1%)

Algorithm
1×egg-herbie
Counts
320 → 320
Iterations

Useful iterations: 0 (71.0ms)

IterNodesCost
049659879
149659879

prune1.3s (7.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New31010320
Fresh6410
Picked101
Done000
Total31714331

Merged error: 7.8b

Counts
331 → 14
Compiler

Compiled 24280 to 15235 computations (37.3% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.4b
(*.f64 (/.f64 t l) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
2.5b
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
3.3b
(*.f64 (/.f64 t l) (sin.f64 k))
14.3b
(*.f64 (*.f64 (/.f64 t l) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite104.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
125×add-exp-log_binary64_461 add-cbrt-cube_binary64_459
78×prod-exp_binary64_472 cbrt-unprod_binary64_456
49×pow1_binary64_484
41×associate-*r/_binary64_365
39×associate-*l/_binary64_366
35×frac-times_binary64_433
32×pow-prod-down_binary64_494
28×associate-*l*_binary64_364
26×add-sqr-sqrt_binary64_445
23×*-un-lft-identity_binary64_423
21×add-cube-cbrt_binary64_458
19×times-frac_binary64_429
18×tan-quot_binary64_582
16×cbrt-undiv_binary64_457 div-exp_binary64_474
11×associate-*r*_binary64_363
8×flip-+_binary64_397 flip3-+_binary64_426
4×*-commutative_binary64_354 add-log-exp_binary64_462
2×div-inv_binary64_420 unswap-sqr_binary64_391
1×distribute-rgt-in_binary64_373 distribute-lft-in_binary64_372 distribute-lft-out_binary64_374
Counts
4 → 176
Calls

4 calls:

32.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
19.0ms
(*.f64 (/.f64 t l) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
13.0ms
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
8.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series1.4s (8.5%)

Counts
4 → 12
Calls

4 calls:

694.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
321.0ms
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
314.0ms
(*.f64 (/.f64 t l) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
99.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

simplify92.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
050845129

prune725.0ms (4.3%)

Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New1844188
Fresh21113
Picked011
Done000
Total18616202

Merged error: 7.8b

Counts
202 → 16
Compiler

Compiled 15795 to 9037 computations (42.8% saved)

regimes260.0ms (1.5%)

Compiler

Compiled 1872 to 1371 computations (26.8% saved)

bsearch189.0ms (1.1%)

Steps
ItersRangePoint
6
9.163044128556979e-116
3.8584035694833476e-115
1.8975220742021813e-115
9
-1.2690279208306966e-235
-7.367777990015376e-245
-3.0717970846058635e-240
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
057132
157132

end0.0ms (0%)

sample4.0s (23.9%)

Algorithm
1×intervals
Results
1.8s2715×body1024valid
532.0ms1248×body512valid
460.0ms3404×body128valid
180.0ms1334×body128invalid
177.0ms626×body256valid
63.0ms154×body512invalid
34.0ms56×body1024invalid
25.0ms93×body256invalid
8.0ms7×body2048valid
Compiler

Compiled 562 to 398 computations (29.2% saved)

Profiling

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